Subgroups — C₂×#6395 #89884

Order 448.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#6395	C₂	1	4	yes	maximal, direct product factor
5	C₂³×D₇	—	2	1	no	—
6	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
7	C₂²×Dic₇	—	2	1	no	—
8	C₂×D₂₈	—	2	1	no	—
9	C₂×D₂₈	—	2	2	no	—
10	C₂×D₂₈	C₄	1	4	yes	complemented
11	C₂×D₂₈	C₂²	1	2	yes	—
12	C₂×C₇×C₈	—	2	2	no	—
13	C₂×C₇×C₈	C₂²	1	2	yes	complemented
14	C₄⋊Dic₇	—	2	1	no	—
15	C₄⋊Dic₇	C₂²	1	2	yes	complemented
16	C₂×#102	—	7	1	no	maximal, Sylow
17	C₂³×C₇	D₄	1	1	yes	characteristic
18	C₂²×D₇	—	2	4	no	—
19	C₂²×D₇	—	2	2	no	—
20	C₂²×D₇	—	4	2	no	—
21	C₂²×D₇	—	4	2	no	—
22	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₇	D₄	1	2	yes	—
25	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
26	C₂×Dic₇	—	2	2	no	—
27	C₂×Dic₇	—	4	2	no	—
28	D₂₈	—	2	4	no	—
29	D₂₈	—	2	2	no	—
30	D₂₈	C₂×C₄	1	4	yes	complemented
31	C₇×C₈	—	2	2	no	—
32	C₂²×D₄	—	7	1	no	—
33	C₂²×C₈	D₇	1	1	yes	characteristic, complemented
34	C₂×C₄⋊C₄	—	7	1	no	—
35	#102	—	7	4	no	—
36	C₂²×C₇	C₂²⋊C₄	1	2	yes	—
37	C₂²×C₇	D₈	1	2	yes	—
38	C₂²×C₇	SD₁₆	1	2	yes	—
39	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
40	C₂×D₇	—	2	4	no	—
41	C₂×D₇	—	4	8	no	—
42	C₂×D₇	—	4	2	no	—
43	C₂×D₇	—	4	2	no	—
44	C₄×C₇	C₂²⋊C₄	1	2	yes	—
45	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
46	C₄×C₇	C₂×D₄	1	1	yes	characteristic
47	Dic₇	—	4	2	no	—
48	C₂⁴	—	14	1	no	—
49	C₂×D₄	—	7	4	no	—
50	C₂×D₄	—	7	2	no	—
51	C₂×D₄	—	14	1	no	—
52	C₂×D₄	—	14	2	no	—
53	C₂²×C₄	—	14	1	no	—
54	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	C₂×D₇	1	2	yes	complemented
57	C₄⋊C₄	—	7	2	no	—
58	C₄⋊C₄	—	14	1	no	—
59	C₂×C₇	#102	1	4	yes	complemented
60	C₂×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₇	C₂×D₈	1	1	yes	characteristic
62	C₂×C₇	C₂×SD₁₆	1	1	yes	characteristic
63	D₇	—	4	4	no	—
64	C₂³	—	14	4	no	—
65	C₂³	—	14	2	no	—
66	C₂³	—	28	2	no	—
67	C₂³	—	28	2	no	—
68	C₂³	D₂₈	1	1	yes	characteristic
69	D₄	—	7	4	no	—
70	D₄	—	14	4	no	—
71	D₄	—	14	2	no	—
72	C₂×C₄	—	14	2	no	—
73	C₂×C₄	—	28	2	no	—
74	C₂×C₄	C₄×D₇	1	2	yes	—
75	C₂×C₄	D₂₈	1	1	yes	characteristic
76	C₂×C₄	C₂²⋊D₇	1	2	yes	—
77	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
78	C₈	—	2	2	no	—
79	C₇	C₂×#102	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	14	4	no	—
81	C₂²	—	28	2	no	—
82	C₂²	—	28	2	no	—
83	C₂²	—	28	8	no	—
84	C₂²	#1132	1	2	yes	—
85	C₂²	D₅₆	1	2	yes	—
86	C₂²	(C₂×D₇)⋊C₄	1	2	yes	—
87	C₂²	C₂×D₂₈	1	1	yes	characteristic
88	C₄	—	28	2	no	—
89	C₄	(C₂×D₇)⋊C₄	1	2	yes	—
90	C₄	C₂×C₄×D₇	1	1	yes	characteristic
91	C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
92	C₂	—	28	4	no	—
93	C₂	#6395	1	4	yes	direct product factor
94	C₂	C₂×#1132	1	1	yes	characteristic
95	C₂	C₂×D₅₆	1	1	yes	characteristic
96	C₂	C₂×(C₂×D₇)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₈
commutator	C₄×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₂²×C₇×C₈	C₂
socle	C₂³×C₇	D₄
prime radical	C₂²×D₂₈	C₂
cosocle	C₂×C₄×C₇	C₂³
hypercenter	C₂²×C₈	D₇
hypocenter	C₇	C₂×#102
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×C₇×C₈	C₂	semidirect
3. C₂×C₄⋊Dic₇	C₂	semidirect
4. #6395	C₂	direct (N × H)
10. C₂×D₂₈	C₄	semidirect
13. C₂×C₇×C₈	C₂²	semidirect
15. C₄⋊Dic₇	C₂²	semidirect
30. D₂₈	C₂×C₄	semidirect
33. C₂²×C₈	D₇	semidirect
56. C₂×C₈	C₂×D₇	semidirect
59. C₂×C₇	#102	semidirect
79. C₇	C₂×#102	semidirect
93. C₂	#6395	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×D₂₈	2
C₂²×C₇×C₈	2
C₂×C₄⋊Dic₇	2
#6395	2
C₂×#102	7

Subgroups — C2×#6395 #89884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6395 #89884